It has been a while since I watched much Bleach; fortunately, the Puyo Puyo wiki has the names spelled out. For the Puyo Puyo characters in shinigami uniform, the wiki lists them as "Division 24", but their names in Japanese seem to say "Puyo Division" and the badge shows a puyo instead of a number (as can be seen on Alex's arm).

Character stats:
https://puyonexus.com/wiki/PPQ:Nelliel_tu_Odelschwanck/%E2%98%856
https://puyonexus.com/wiki/PPQ:Uryu_Ishida/%E2%98%856
https://puyonexus.com/wiki/PPQ:Alex_ver._Division_24/%E2%98%856
https://puyonexus.com/wiki/PPQ:Grimmjow_Jaegerjaques/%E2%98%856
https://puyonexus.com/wiki/PPQ:Ulquiorra_Cifer/%E2%98%856
https://puyonexus.com/wiki/PPQ:Risukuma_ver._Division_24/%E2%98%856
https://puyonexus.com/wiki/PPQ:After_Training_Ichigo_Kurosaki/%E2%98%856
https://puyonexus.com/wiki/PPQ:Dark_Schezo_ver._Division_24/%E2%98%856